The mayor said it was time to treat the capital as a "grown-up" and be given complete control over property taxes and business rates.
He backed a report that also called for a "tourist tax" and more borrowing powers for London.
But there was a warning that the rest of the country risked being left behind if London continues to plough ahead.
"The danger is that London powers ahead, and becomes even more the place to do business, and gets even further ahead of the other regions," said a spokesman for the Institute for Public Policy Research North.
"It puts the pressure on other parts of the country to get their act together."
Johnson said the current way London received funding from central government was "simply not fit for purpose" and said it was time to treat London in a more "grown up" and "mature" way.
He said there was an "acute need for London to be able to better plan and finance the infrastructure needed to prosper and maintain a great quality of life, in the face of a decade of expansion".
"The current system is simply not fit for purpose and is out of step with the funding settlements enjoyed by cities of comparable size and stature.
"Furthermore, Londoners will increasingly question why London government cannot enjoy similar fiscal freedoms as those afforded to the devolved governments in Scotland and Wales," he added.
The mayor's comments come after the report, which he commissioned, recommended giving the city the power to introduce new taxes, such as a levy on tourists, and greater freedom to borrow.
Under the proposals London would be given complete control over property taxes, including council tax, stamp duty and business rates.
Professor Tony Travers from the London School of Economics, who chaired the report, said: "London needs greater financial autonomy to drive growth and deliver better infrastructure.
"Wales and, in particular, Scotland are moving towards far greater discretion over taxes. London should be treated similarly."
Peter Bishop, deputy chief executive of the London Chamber of Commerce and Industry (LCCI), described the report as "a welcome and thoughtful contribution to the debate on how to secure London's future economic prosperity".
The Taxpayers' Alliance agreed, saying: "The current situation where local politicians are responsible for spending money but not for collecting it through taxation encourages irresponsible behaviour."
Ending the north-south divide is seen as critical to the economic recovery. London and South East are leaving parts of the north trailing in terms of property prices, jobs and investment.
The coalition has championed the idea of elected mayors in other major cities, but only Bristol voted in favour when referendums were held a year ago.
There have been calls for a 'Boris for the north' to fight for the regions and allow them to compete with London.